The existence of positive solutions for a class of indefinite weight semilinear elliptic problems with critical Sobolev exponent
type: Item
instance of: scholarly article
title: The existence of positive solutions for a class of indefinite weight semilinear elliptic problems with critical Sobolev exponent
zbMATH Open document ID: 1096.35051
author: Bongsoo Ko
published in: Taiwanese Journal of Mathematics
publication date: 2004-09-28T00:00:00Z
review text: The author discusses the existence of positive solutions of the following boundary value problems: \[ \begin{cases} -\Delta u=\lambda g(x)f(u) \quad &\text{in }\Omega\\ u=0\quad &\text{on }\partial\Omega, \end{cases}\tag{1} \] where \(\lambda\) is a real parameter, \(\Omega\) is an open bounded domain in \(\mathbb{R}^N\), \(N\geq 3\), with the smooth boundary. The author considers the critical exponent case \(f(u)=u(1+ |u|^p)\) with \(p=\frac{4}{N-2}\). The function \(g,g:\overline\Omega \to\mathbb{R}^1\) is smooth and changes sign.
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 35B33
Mathematics Subject Classification ID: 35J20
Mathematics Subject Classification ID: 47J30
zbMATH DE Number: 2104154
zbMATH Keywords: indefinite weight
zbMATH Keywords: positive solution
zbMATH Keywords: critical exponent
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.11650/twjm/1500558458
OpenAlex ID: W4237110501
DOI: 10.11650/TWJM/1500558458
Recommended article: ON POSITIVE SOLUTIONS FOR A CLASS OF INDEFINITE WEIGHT SEMILINEAR ELLIPTIC BOUNDARY VALUE PROBLEMS WITH CRITICAL SOBOLEV EXPONENT
Recommended article: The existence of positive solutions for a class of indefinite weight semilinear elliptic boundary value problems
Recommended article: Q4948306
Recommended article: Q4817902
Recommended article: Positive solutions for semilinear elliptic equations with critical weighted Hardy-Sobolev exponents
Recommended article: Positive solutions for some semilinear elliptic equations with critical sobolev exponents
Recommended article: Q3104369
Recommended article: The existence of a positive solution of semilinear elliptic equations with limiting Sobolev exponent
Recommended article: Q5390099
Recommended article: Existence of positive solutions for a semilinear elliptic problem with critical Sobolev and Hardy terms
description: scientific article; zbMATH DE number 2104154